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Product of Elements in Array.
ar_a <- c(1,2,3)
ar_b <- c(1,2,3,4)
prod(ar_a)## [1] 6prod(ar_b)## [1] 24ar_a <- c(1,2,3)
ar_b <- c(1,2,3/1,2,3)
rep(0, length(ar_a))## [1] 0 0 0First, we will generate an NaN matrix with 3 rows and 3 columnes.
mt_x <- array(NA, dim=c(3, 3))
dim(mt_x)## [1] 3 3print(mt_x)## [,1] [,2] [,3]
## [1,] NA NA NA
## [2,] NA NA NA
## [3,] NA NA NASecond, we will generate a matrix with 2 rows and four columns.
mt_x <- array(c(1, 1.5, 0, 2, 0, 4, 0, 3), dim=c(2, 4))
dim(mt_x)## [1] 2 4print(mt_x)## [,1] [,2] [,3] [,4]
## [1,] 1.0 0 0 0
## [2,] 1.5 2 4 3First, we will create a three dimensional array with the same data as what was used to create the 2-dimensional array on top.
# Multidimensional Array
# 1 is r1c1t1, 1.5 in r2c1t1, 0 in r1c2t1, etc.
# Three dimensions, row first, column second, and tensor third
x <- array(c(1, 1.5, 0, 2, 0, 4, 0, 3), dim=c(2, 2, 2))
dim(x)## [1] 2 2 2print(x)## , , 1
##
## [,1] [,2]
## [1,] 1.0 0
## [2,] 1.5 2
##
## , , 2
##
## [,1] [,2]
## [1,] 0 0
## [2,] 4 3Second, in the example below, we will generate a 3-dimensional array. The first dimension corresponds to different income levels, the second marital status, and the third the number of kids.We compute in the example below taxable income in 2008 given income levels given IRS rules.
# A, Income Array
ar_income <- seq(0,200000,length.out=3)
# B. Exemptions and Deductions
fl_exemption <- 3500# exemption amount per household member
mt_deduction <- matrix(data=NA, nrow=2, ncol=5)# Marital-status and number of children-specific deduction
mt_deduction[1,1] <- 5450# Single filers
mt_deduction[1,2:5] <- 8000# Single filer with children
mt_deduction[2,] <- 10900# Married couples filing jointly
# C. Taxable Income
mn_taxable_income <- array(NA, dim=c(length(ar_income), 2, 5))
for (y in 1:length(ar_income)){
for (m in 1:2){
for (k in 0:4){
mn_taxable_income[y,m,k+1] <- ar_income[y]-fl_exemption*m-fl_exemption*k-mt_deduction[m,k+1]
}
}
}
# D. Name dimensions
dimnames(mn_taxable_income)[[1]] = paste0('income=', round(ar_income, 0))
dimnames(mn_taxable_income)[[2]] = paste0('married=', 0:1)
dimnames(mn_taxable_income)[[3]] = paste0('kids=', 0:4)
# E. Print
dim(mn_taxable_income)## [1] 3 2 5print(mn_taxable_income)## , , kids=0
##
## married=0 married=1
## income=0 -8950 -17900
## income=1e+05 91050 82100
## income=2e+05 191050 182100
##
## , , kids=1
##
## married=0 married=1
## income=0 -15000 -21400
## income=1e+05 85000 78600
## income=2e+05 185000 178600
##
## , , kids=2
##
## married=0 married=1
## income=0 -18500 -24900
## income=1e+05 81500 75100
## income=2e+05 181500 175100
##
## , , kids=3
##
## married=0 married=1
## income=0 -22000 -28400
## income=1e+05 78000 71600
## income=2e+05 178000 171600
##
## , , kids=4
##
## married=0 married=1
## income=0 -25500 -31900
## income=1e+05 74500 68100
## income=2e+05 174500 168100There is an array with M elements, get N elements from the M elements.
First cut including the starting and ending points.
it_M <- 5
it_N <- 4
ar_all_elements = seq(1,10,10)Select elements with direct indexing, or with head and tail functions. Get the first two elements of three elements array.
# Remove last element of array
vars.group.bydf <- c('23','dfa', 'wer')
vars.group.bydf[-length(vars.group.bydf)]## [1] "23" "dfa"# Use the head function to remove last element
head(vars.group.bydf, -1)## [1] "23" "dfa"head(vars.group.bydf, 2)## [1] "23" "dfa"Get last two elements of array.
# Remove first element of array
vars.group.bydf <- c('23','dfa', 'wer')
vars.group.bydf[2:length(vars.group.bydf)]## [1] "dfa" "wer"# Use Tail function
tail(vars.group.bydf, -1)## [1] "dfa" "wer"tail(vars.group.bydf, 2)## [1] "dfa" "wer"Select all except for the first and the last element of an array.
# define array
ar_amin <- c(0, 0.25, 0.50, 0.75, 1)
# select without head and tail
tail(head(ar_amin, -1), -1)## [1] 0.25 0.50 0.75Select the first and the last element of an array. The extreme values.
# define array
ar_amin <- c(0, 0.25, 0.50, 0.75, 1)
# select head and tail
c(head(ar_amin, 1), tail(ar_amin, 1))## [1] 0 1# Convert Inf and -Inf to NA
x <- c(1, -1, Inf, 10, -Inf)
na_if(na_if(x, -Inf), Inf)## [1] 1 -1 NA 10 NAHandling numbers with real and imaginary components. Two separate issues, given an array of numbers that includes real as well as imaginary numbers, keep subset that only has real components. Additionally, for the same array, generate an equal length version of the array that includes the real components of all numbers.
Define complex numbers.
# Define a complex number
cx_number_a <- 0+0.0460246857561777i
# Define another complex number
cx_number_b <- complex(real = 0.02560982, imaginary = 0.0460246857561777)
# An array of numbers some of which are complex
ar_cx_number <- c(0.02560982+0.000000000i, 0.00000000+0.044895305i,
0.00000000+0.009153429i, 0.05462045+0.000000000i,
0.00000000+0.001198538i, 0.00000000+0.019267050i)Extract real components from a complex array.
# equi-length real component
ar_fl_number_re <- Re(ar_cx_number)
print(ar_fl_number_re)## [1] 0.02560982 0.00000000 0.00000000 0.05462045 0.00000000 0.00000000# equi-length img component
ar_fl_number_im <- Im(ar_cx_number)
print(ar_fl_number_im)## [1] 0.000000000 0.044895305 0.009153429 0.000000000 0.001198538 0.019267050Keep only real elements of array.
# subset of array that is real
ar_fl_number_re_subset <- Re(ar_cx_number[Re(ar_cx_number)!=0])
print(ar_fl_number_re_subset)## [1] 0.02560982 0.05462045We have a sequence of integers, some positive and some negative. We convert this into a string array, and append positive sign in front of positive values.
# An array of integers
ar_it_vals <- seq(-5, 5, by = 1)
# Add positive sign in front of positive and zero elements
st_it_vals <- paste0(ar_it_vals)
st_it_vals[ar_it_vals>0] <- paste0("+", st_it_vals[ar_it_vals>0])
st_it_vals[ar_it_vals==0] <- paste0("±", st_it_vals[ar_it_vals==0])
# Display
print(st_it_vals)## [1] "-5" "-4" "-3" "-2" "-1" "±0" "+1" "+2" "+3" "+4" "+5"First, we demonstrate how purrr::reduce() works with a simple summation example. We use the addition operator.
# Using R pipe operator
# 1 + 2 + 3 = 6
fl_sum <- 1:3 |> purrr::reduce(`+`)
print(fl_sum)## [1] 6Second, what if there is an NA value? NA will be ignored, we will write a custom function. The custom function, to work with reduce, should be such that it is “a binary function that takes two values and returns a single value”.
# define sum function that ignores NA
sum_ignore_na <- function(x,y) {
if (!is.na(x) && !is.na(y)) {
x + y
} else if (is.na(x)) {
y
} else if (is.na(y)) {
x
} else {
NA
}
}
# Using R pipe operator
# 1 + 10 + 1 = 12
fl_sum <- c(1, 10, NA, 1) |> purrr::reduce(sum_ignore_na)
print(fl_sum)## [1] 12